Built on

S. Hollands, On the modular operator of mutli-component regions in chiral CFT , 1904.08201
Original
1904
Earlier work this paper cites.
S. Dutta and T. Faulkner, A canonical purification for the entanglement wedge cross-section , 1905.00577
Original
1905
Earlier work this paper cites.
H. Casini, M. Huerta, J. M. Magán and D. Pontello, Entanglement entropy and superselection sectors. Part I. Global symmetries , JHEP 02
Original
1905
Earlier work this paper cites.
Y. Kusuki and K. Tamaoka, Dynamics of Entanglement Wedge Cross Section from Conformal Field Theories , 1907.06646
Original
1907
Earlier work this paper cites.
H.-S. Jeong, K.-Y. Kim and M. Nishida, Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction , JHEP 12
Original
1909
Earlier work this paper cites.
Y. Kusuki and K. Tamaoka, Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench , JHEP 02
Original
1909
Earlier work this paper cites.
N. Bao and N. Cheng, Multipartite Reflected Entropy , JHEP 10
Original
1909
Earlier work this paper cites.
J. Chu, R. Qi and Y. Zhou, Generalizations of Reflected Entropy and the Holographic Dual , 1909.10456
Original
1909
Earlier work this paper cites.
D. Marolf, CFT sewing as the dual of AdS cut-and-paste , JHEP 02
Original
1909
Earlier work this paper cites.
R. Longo and F. Xu, Von Neumann Entropy in QFT , Communications in Mathematical Physics (Feb., 2020) , [ 1911.09390 ]
Original
1911
Earlier work this paper cites.
C. Akers and P. Rath, Entanglement Wedge Cross Sections Require Tripartite Entanglement , 1911.07852
Original
1911
Earlier work this paper cites.
S. Doplicher, R. Haag and J. E. Roberts, Fields, observables and gauge transformations I , Commun. Math. Phys. 13
1969
Earlier work this paper cites.
D. Buchholz, Product states for local algebras , Commun. Math. Phys. 36
1974
Earlier work this paper cites.
S. Doplicher, Local aspects of superselection rules , Commun. Math. Phys. 85
1982
Earlier work this paper cites.
S. Doplicher and R. Longo, Local aspects of superselection rules. II , Commun. Math. Phys. 88
1983
Earlier work this paper cites.

Similar

S. Doplicher and R. Longo, Standard and split inclusions of von Neumann algebras , Invent. Math. 75
1984
Cited alongside, same era.
D. Buchholz and E. H. Wichmann, Causal Independence and the Energy Level Density of States in Local Quantum Field Theory , Commun. Math. Phys. 106
1986
Cited alongside, same era.
D. Buchholz, S. Doplicher and R. Longo, On Noether’s Theorem in Quantum Field Theory , Annals Phys. 170
1986
Cited alongside, same era.
R. Dijkgraaf, C. Vafa, E. P. Verlinde and H. L. Verlinde, The Operator Algebra of Orbifold Models , Commun. Math. Phys. 123
1989
Cited alongside, same era.
R. Longo, Index of subfactors and statistics of quantum fields. I , Commun. Math. Phys. 126
1989
Cited alongside, same era.
Springer, 1992

Then

H. Casini, Entropy inequalities from reflection positivity , J. Stat. Mech. 1008
Original
2010
Later among the works it cites.
R. Longo, P. Martinetti and K.-H. Rehren, Geometric modular action for disjoint intervals and boundary conformal field theory , Rev. Math. Phys. 22
Original
2010
Later among the works it cites.
L. Lepori, G. De Chiara and A. Sanpera, Scaling of the entanglement spectrum near quantum phase transitions , Physical Review B 87
Original
2013
Later among the works it cites.
J. Cardy, Some results on the mutual information of disjoint regions in higher dimensions , J. Phys. A46
Original
2013
Later among the works it cites.
H. Casini, M. Huerta, R. C. Myers and A. Yale, Mutual information and the F-theorem , JHEP 10

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2020

Reflected entropy, symmetries and free fermions

Bueno, Pablo, Casini, Horacio

Understand

Exploiting the split property of quantum field theories (QFTs), a notion of von Neumann entropy associated to pairs of spatial subregions has been recently proposed both in the holographic context -- where it has been argued to be related to the entanglement wedge cross section -- and for general QFTs.

We argue that the definition of this "reflected entropy" can be canonically generalized in a way which is particularly suitable for orbifold theories -- those obtained by restricting the full algebra of operators to those which are neutral under a global symmetry group.
This turns out to be given by the full-theory reflected entropy minus an entropy associated to the expectation value of the "twist" operator implementing the symmetry operation.
Then we show that the reflected entropy for Gaussian fermion systems can be simply written in terms of correlation functions and we evaluate it numerically for two intervals in the case of a two-dimensional Dirac field as a function of the conformal cross-ratio.

Built on

S. Hollands, On the modular operator of mutli-component regions in chiral CFT , 1904.08201
Original
1904
Earlier work this paper cites.
S. Dutta and T. Faulkner, A canonical purification for the entanglement wedge cross-section , 1905.00577
Original
1905
Earlier work this paper cites.
H. Casini, M. Huerta, J. M. Magán and D. Pontello, Entanglement entropy and superselection sectors. Part I. Global symmetries , JHEP 02
Original
1905
Earlier work this paper cites.
Y. Kusuki and K. Tamaoka, Dynamics of Entanglement Wedge Cross Section from Conformal Field Theories , 1907.06646
Original
1907
Earlier work this paper cites.
H.-S. Jeong, K.-Y. Kim and M. Nishida, Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction , JHEP 12
Original
1909
Earlier work this paper cites.
Y. Kusuki and K. Tamaoka, Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench , JHEP 02
Original
1909
Earlier work this paper cites.
N. Bao and N. Cheng, Multipartite Reflected Entropy , JHEP 10
Original
1909
Earlier work this paper cites.
J. Chu, R. Qi and Y. Zhou, Generalizations of Reflected Entropy and the Holographic Dual , 1909.10456
Original
1909
Earlier work this paper cites.
D. Marolf, CFT sewing as the dual of AdS cut-and-paste , JHEP 02
Original
1909
Earlier work this paper cites.
R. Longo and F. Xu, Von Neumann Entropy in QFT , Communications in Mathematical Physics (Feb., 2020) , [ 1911.09390 ]
Original
1911
Earlier work this paper cites.
C. Akers and P. Rath, Entanglement Wedge Cross Sections Require Tripartite Entanglement , 1911.07852
Original
1911
Earlier work this paper cites.
S. Doplicher, R. Haag and J. E. Roberts, Fields, observables and gauge transformations I , Commun. Math. Phys. 13
1969
Earlier work this paper cites.
D. Buchholz, Product states for local algebras , Commun. Math. Phys. 36
1974
Earlier work this paper cites.
S. Doplicher, Local aspects of superselection rules , Commun. Math. Phys. 85
1982
Earlier work this paper cites.
S. Doplicher and R. Longo, Local aspects of superselection rules. II , Commun. Math. Phys. 88
1983
Earlier work this paper cites.

Similar

S. Doplicher and R. Longo, Standard and split inclusions of von Neumann algebras , Invent. Math. 75
1984
Cited alongside, same era.
D. Buchholz and E. H. Wichmann, Causal Independence and the Energy Level Density of States in Local Quantum Field Theory , Commun. Math. Phys. 106
1986
Cited alongside, same era.
D. Buchholz, S. Doplicher and R. Longo, On Noether’s Theorem in Quantum Field Theory , Annals Phys. 170
1986
Cited alongside, same era.
R. Dijkgraaf, C. Vafa, E. P. Verlinde and H. L. Verlinde, The Operator Algebra of Orbifold Models , Commun. Math. Phys. 123
1989
Cited alongside, same era.
R. Longo, Index of subfactors and statistics of quantum fields. I , Commun. Math. Phys. 126
1989
Cited alongside, same era.
Springer, 1992